I've got hold of my dad's 1978 Balladeer, and noticed that it's got a slight problem on the higher frets of the high e string.

The offenders are the 10th, 11th 12th and 14th - the thirst three sound the 13th fret note, and the 14th fret sounds the 15th fret note..?

The frets aren't damaged at all, so is this to do with the neck? Can I adjust anything to remove the problem?
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Your intonation could be out
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Sounds like the 13th and 15th frets are high so that when you fret behind them they touch those frets too.
Those frets may need to be either filed down a little or reseated. COuld be an issue with the neck but I can't tell. A good Luthier/Tech will be able to diagnose and fix the problem though.
It could be raised frets as said before.

Worst case scenario is the neck wood at that point has warped. In which case you should seek proffesional attention.
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